Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}4x+y &= -1 \\ -4x-8y &= 8\end{align*}$
Solution: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-8y = 4x+8$ Divide both sides by $-8$ to isolate $y$ $y = {-\dfrac{1}{2}x - 1}$ Substitute this expression for $y$ in the first equation. $4x+({-\dfrac{1}{2}x - 1}) = -1$ $4x - \dfrac{1}{2}x - 1 = -1$ Simplify by combining terms, then solve for $x$ $\dfrac{7}{2}x - 1 = -1$ $\dfrac{7}{2}x = 0$ $x = 0$ Substitute $0$ for $x$ back into the top equation. $4( 0)+y = -1$ $y = -1$ $y = -1$ $y = -1$ The solution is $\enspace x = 0, \enspace y = -1$.